## A precision and range independent tool for testing floating-point arithmetic I: basic operations, square root and remainder (1999)

Citations: | 2 - 0 self |

### BibTeX

@MISC{Verdonk99aprecision,

author = {Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren},

title = {A precision and range independent tool for testing floating-point arithmetic I: basic operations, square root and remainder},

year = {1999}

}

### OpenURL

### Abstract

This paper introduces a precision and range independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, o#ering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations.

### Citations

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Citation Context ...vector: 3c ALL 1 0 OK 1 A simple test vector The leading character is the version number. It can be either `2' or `3', indicating that the test vector is taken from version 2, respectively 3, of the [=-=Coonen 1984-=-] test suite, `H' indicating that it is taken from [Hough et al. 1988] while `A' indicates that the test vector is new and was added by the authors. The operator, denoted by `c', stands for `copy from... |

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Citation Context ... floating-point standards, algorithms for correctly rounded conversion between decimal strings and binary floating-point formats have become available which incur little time penalty in common cases [=-=Gay 1990-=-]. Our test tool has taken this evolution into account. With the option -ieee, the driver program considers only those vectors in our conversion test set with operands lying in the range within which ... |

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Citation Context ...e applied it on one hand to hardware floating-point implementations, including the Intel Pentium processors and SUN Sparc stations, and on the other hand to the multiprecision software library FMLIB [=-=Smith 1991-=-] and our own IEEE compliant multiprecision floatingpoint implementation MpIeee [Verschaeren and Cuyt 1999]. The results of testing the basic operations +; \Theta; =; p and remainder in these floating... |

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2 |
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Citation Context ...iguous. For remainder, the operator at the language level may not be bound to the IEEE-compliant remainder function available in hardware, but rather to a modulo function which is not IEEE compliant [=-=ANSI-ISO-IEC 1990-=-]. For conversions, this binding becomes even looser and hence the distinction between what is actually being tested, the language binding or the effectively available implementation, becomes essentia... |

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2 |
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Citation Context ...duced a comprehensive, precision and range independent tool to test how well a floating-point implementation with arbitrary precision and exponent range complies with the philosophy of the IEEE--754 [=-=IEEE 1985-=-] and IEEE--854 [IEEE 1987] standards. As pointed out in greater detail in [Cuyt et al. 1999], the motivation for the development of such a tool is the ever increasing need in many applications for mo... |

2 |
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Citation Context ...d vice versa stand out from the other conversions in IEEE-754 and IEEE-854 in that these conversions need not be correctly rounded for all ranges of operands. Full details can be found in [IEEE 1985; =-=IEEE 1987-=-]. However, since the publication of the IEEE floating-point standards, algorithms for correctly rounded conversion between decimal strings and binary floating-point formats have become available whic... |

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Citation Context ...mal numbers are posted in [Tydeman 1996] which require a lot more than 53 bits to achieve correct rounding to double precision binary representation. These tables correspond with results obtained in [=-=Paxson and Kahan 1991-=-]. There, the authors describe algorithms to find numbers in an input base (2 or 10) which, in the output base, lie extremely close to representable numbers (for directed roundings) , or exactly half-... |

2 |
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Citation Context ...coming Fortran 2000 standard. SUN Sparc is a single/double-based architecture, providing single and double precision hardware as well as quadruple precision floating-point arithmetic in software [SUN =-=Microsystems 1997-=-]. These three formats can be addressed in Fortran 90 by the real(kind(0.0)), real(kind(0.D0)) and real(kind(0.Q0)) type declarations respectively. Alternatively, one can use the real(4), real(8) and ... |

2 | A test for correctly rounded SQRT. http://http.cs.berkeley.edu/˜ wkahan/SQRTest.ps - Kahan - 1996 |

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1 |
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Citation Context ...[ANSI-ISO-IEC 1999], these specifications were not compatible with the specifications for floating-point$hardware integer conversion in C/C++ nor are they compatible with the Fortran 90/95 standards [=-=ANSI-ISO-IEC 1991-=-; ANSIISO -IEC 1997]. Hence, IEEE compliant conversions from floating-point to integer formats are still often unavailable at the programming language level. It should be observed that, probably for t... |

1 |
Information Technology - Programming Languages - C
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Citation Context ... 1 Round to nearest except for exact halfway cases which are rounded away from zero 18 \Delta A. Cuyt, B. Verdonk, and D. Verschaeren features as in Table 2, but now for the C/C++ language standards [=-=ANSI-ISO-IEC 1998-=-; ANSI-ISO-IEC 1999]. Here again we use slanted font to indicate compiler specific features. Where the recent C standard is specific about rounding, it requires language support for the conversion in ... |

1 |
Chapter 5: Floating-point c extensions
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(Show Context)
Citation Context ...the conversion in all rounding modes, as can be seen from Table 3. This too, is a major and welcome addition to the previous C standard and a result of the efforts of the Numerical C Extension Group [=-=Thomas 1995-=-]. It should be specified, however, that the functions lrint and llrint and their single and extended precision equivalents, convert to signed integers only. For conversion to unsigned integers, the r... |

1 |
Decimal to binary conversion for IEEE 754/854 double format. Posting to the reliable computing@interval.usl.edu mailing list on 25
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Citation Context ... warning rather than an error in case the operand is outside the IEEE range. Whereas no test set for decimal $ binary conversion is included in [Coonen 1984], tables of decimal numbers are posted in [=-=Tydeman 1996-=-] which require a lot more than 53 bits to achieve correct rounding to double precision binary representation. These tables correspond with results obtained in [Paxson and Kahan 1991]. There, the auth... |

1 | Floating-point arithmetic in future supercomputers - Verdonk, Cuyt, et al. - 1989 |

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1 | Introductions to the special issue on verification of arithmetic hardware - German - 1999 |